You are getting the spaces because you are stringifying the array. Try

foreach my $file (@filenames) {
    open (INFILE, "$file") || die ("Can't open file $file$!");
    @all=<INFILE>;
    close (INFILE);
   print OUTFILE1 @all;
}
[download]

or better yet

foreach my $file (@filenames) {
    open (INFILE, "$file") || die ("Can't open file $file$!");
    print OUTFILE1 <INFILE>;
    close (INFILE);
}
[download]